I was trying this mod out and when I controlled an avatar, went into the control center my character is sitting in, left and disconnected, the game crashed with this message:

The mod Avatars (0.5.17) caused a non-recoverable error.
Please report this error to the mod author.

Error while running event Avatars::on_gui_click (ID 1)
LuaEntity API call when LuaEntity was invalid.
stack traceback:
[C]: in function 'index'
__Avatars/scripts/avatar_control.lua:50: in function 'bodySwap'
Avatars/scripts/avatar_control.lua:175: in function 'loseAvatarControl'
Avatars/control.lua:111: in function <Avatars/control.lua:59>

If I just connect to the avatar and leave, it's fine. Its the act of entering and leaving the control center with the avatar that breaks the game, when disconnecting. I am not sure if this also happens with an empty control center.

Hm, I'm not able to reproduce this. Just to verify your steps:

1. Enter control center with player and control an avatar
2. Enter the same control center as avatar
3. Leave control center as avatar
4. Disconnect from avatar
5. Game crash?

Is this the first time you've used the mod in this save? Do you have any other mods enabled?

This is exactly how I got it. I just tested it again to be sure. I do have a long list of mods, the biggest beeing Space Exploration. I made a little test setup with editor extensions and tested Avatars with everything and it crashed, as expected. Just with Space Exploration it doesnt crash, so thats not it.

I have now boiled it down to Gizmo's car keys. Doing these steps, while having this mod active, crashes the game.

Another thing: There is a new mod in town: https://mods.factorio.com/mod/Kruise_Kontrol/discussion/6071fc5da0a7c369a4cb829f
It currently does not work with Avatars but it might be cool if it did. It makes the character path to a selected location on its own or auto mine trees or ore. Currently weird things happen when you try to do these things as an avatar. I also mentioned that in a post at the mod.

You're correct, the crash is an issue with Gizmo's car keys, it deletes your original character. I have entered a bug for it on it's page: https://mods.factorio.com/mod/GCKI/discussion/6074ddc8ada1100252bcd08d

As for Kruise Kontrol, I don't do anything with the avatars besides on build or when you change control, so any weird things happening are likely on it's end.